Preheat the oven to 220°C / 425°F. High oven heat is key for getting the fries crispy and for finishing the chicken quickly without drying it.

Prep the fries: Place the cut potatoes in a large bowl of cold water and rinse until the water runs clear, then soak 10 minutes. This removes excess surface starch so they crisp rather than glue together when roasted.

Parboil the potatoes: Drain and transfer the potatoes to a pot of salted cold water. Bring to a gentle boil and cook 5 minutes — they should be just starting to soften but not falling apart. Parboiling gelatinizes the interior starch so the outside can crisp without the center staying hard.

Drain the parboiled fries and spread them on a clean kitchen towel or baking sheet to steam-dry for 5 minutes. Removing surface moisture allows the oil to make a crisp crust instead of steaming the potato.

Season the chicken: Pat the thighs very dry with paper towels (moisture prevents browning). Rub each thigh with 1 tsp kosher salt, 1/2 tsp black pepper and the smoked paprika. Tuck rosemary sprigs under the skin where possible and zest half the lemon over the thighs. Dry skin plus direct salt and heat produce the best golden, crackly skin.

Sear the chicken: Heat a large ovenproof skillet over medium-high heat and add 1 tbsp olive oil. When shimmering, place the thighs skin-side down and press lightly to ensure even contact. Sear without moving for 6–8 minutes until the skin is deeply golden and the fat has rendered. Searing develops Maillard flavors (browned, savory compounds) that make the dish taste rich and complex.

Flip and transfer to oven: Turn the thighs skin-side up, add two smashed rosemary sprigs around the chicken, and immediately transfer the skillet to the preheated oven for 12–15 minutes, until an instant-read thermometer inserted into the thickest part near the bone reads 74°C / 165°F. Finishing in the oven cooks evenly without burning the skin.

Toss and roast the fries: While chicken is in the oven, toss the parboiled and dried fries in a large bowl with 3 tbsp olive oil and 1 tsp kosher salt, spreading into a single layer on a rimmed baking sheet. Roast on the top rack for 25–30 minutes, flipping once halfway through, until edges are browned and crisp. The high heat and single layer ensure maximum browning.

Make the pan sauce: When the chicken comes out of the oven, transfer thighs to a plate to rest (resting allows juices to redistribute). Place the skillet over medium heat, add 1 tbsp butter and the sliced onion. Sauté 3–4 minutes until translucent to pick up all browned bits (fond) from the pan — those bits are flavor gold. Add the minced garlic and cook 30 seconds to bloom its aroma.

Deglaze and finish sauce: Pour in the chicken stock and the juice from the other half of the lemon, scraping the bottom of the pan to release fond. Simmer 2–3 minutes to reduce slightly, then swirl in the remaining 1 tbsp butter off the heat to add silkiness and sheen. Taste and adjust seasoning with pepper and a pinch of salt if needed. This quick pan sauce concentrates savory flavors from the browned chicken.

Cook the vegetables: While the sauce is reducing, heat a separate large skillet over medium heat with 1 tbsp butter and 1 tsp olive oil. Add the carrots and sauté 3 minutes, then add the green beans and a pinch of salt. Cook 4–6 minutes until bright and just tender — you want them to keep a little snap for texture contrast with the fries and chicken. Add a squeeze of lemon and a pinch of black pepper to finish.

Plate and finish: Divide fries among 4 plates, place a chicken thigh on each, spoon warm pan sauce and onions over the chicken, and arrange the garlic-butter vegetables alongside. Sprinkle chopped parsley and a little extra lemon zest over the top for freshness and visual lift.

Serve at once: Serve immediately so the skin stays crisp and the fries retain their crunch. Leftovers can be refrigerated and reheated (see tips).